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On Absolute Uniform Retracts, Uniform Approximation Property and Super Weakly Compact Sets of Banach Spaces

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Abstract

In this paper, we show that every super weakly compact convex subset of a Banach space is an absolute uniform retract, and that it also admits the uniform compact approximation property. These can be regarded as extensions of Lindenstrauss and Kalton’s corresponding results.

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Acknowledgements

We thank the referees for their time and comments.

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Authors and Affiliations

  1. School of Mathematical Sciences, Xiamen University, Xiamen, 361005, P. R. China

    Li Xin Cheng, Qing Jin Cheng & Jian Jian Wang

Authors
  1. Li Xin Cheng
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  2. Qing Jin Cheng
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  3. Jian Jian Wang
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Corresponding author

Correspondence to Qing Jin Cheng.

Additional information

Support by National Natural Science Foundation of China (Grant Nos. 11731010, 12071389)

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Cheng, L.X., Cheng, Q.J. & Wang, J.J. On Absolute Uniform Retracts, Uniform Approximation Property and Super Weakly Compact Sets of Banach Spaces. Acta. Math. Sin.-English Ser. 37, 731–739 (2021). https://doi.org/10.1007/s10114-021-0273-1

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  • DOI: https://doi.org/10.1007/s10114-021-0273-1

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